Signal Separation

1. A method of separating a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, each source signal having a respective period similar or equal to p, the method comprising using a computer apparatus to perform the steps of: (a) expressing the composite signal as a matrix having rows each of which is a respective segment of signal amplitude values and corresponds to a length of time associated with a signal cyclet; (b) implementing a decomposition of the matrix by decorrelation and normalisation to obtain decomposition results; and (c) performing independent component analysis (ICA) of the decomposition results to obtain at least one of estimated separated signal modulation envelopes and estimated separated signal cyclets.

2. A method according to claim 1 including the step of estimating source signal period p by synchronous averaging of the composite signal.

3. A method according to claim 1 wherein the decomposition is a singular value decomposition generating decomposition results comprising two singular vector matrices and a singular value matrix, and the step of performing ICA uses one of the singular vector matrices to obtain a rotation matrix and calculates at least one of an independent component matrix and an associated component matrix one of which matrices contains estimated separated signal modulation envelopes and the other contains estimated separated cyclets.

4. A method according to claim 3 wherein the signal modulation envelopes are more statistically independent than the cyclets and step (c) includes processing a singular vector matrix of signal amplitudes to obtain a rotation matrix and calculating an independent component matrix containing estimated separated signal envelopes and a matrix containing estimated separated cyclets.

5. A method according to claim 3 wherein the cyclets are more statistically independent than the signal envelopes and step (c) includes processing a singular vector matrix of cyclets to obtain a rotation matrix and calculating an independent component matrix containing estimated separated cyclets and a matrix containing estimated separated signal envelopes.

6. A method according to claim 1 wherein the composite signal is detected by a single sensor.

7. A method according to claim 1 including detecting the source signals using a plurality of sensors each of which provides a respective composite signal from which a respective matrix is obtained and analysed in steps (a) to (c).

8. A method according to claim 1 including detecting the source signals using a plurality of sensors providing respective composite signals, and the matrix is obtained from the composite signals collectively.

9. A method according to claim 1 for apparatus condition monitoring, the source signals being obtained with the aid of at least one sensor from a plurality of apparatus sources, and the at least one of estimated separated signal modulation envelopes and estimated separated signal cyclets being analysed for indications as to the condition of respective apparatus sources.

10. Computer apparatus for separating a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, the source signals having periodicities similar or equal to p, the computer apparatus being programmed to: (a) express the composite signal as a matrix having rows each of which is a respective segment of signal amplitude values and corresponding to a length of time associated with a signal cyclet; (b) decompose the matrix by decorrelation and normalisation to obtain decomposition results; and (c) perform independent component analysis (ICA) of the decomposition results to obtain at least one of estimated separated signal modulation envelopes and estimated separated signal cyclets.

11. Computer apparatus for separating a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, the source signals having periodicities similar or equal to p, and the computer apparatus being programmed to: (a) partition the composite signal into a plurality of partition matrices having rows each of which is a respective segment of signal amplitude values and corresponds to a length of time associated with a signal cyclet; (b) perform a singular value decomposition (SVD) of at least one of the matrices to obtain two singular vector matrices and a singular value matrix; (c) estimate a true period p of the source signals from an average of data within rows of the partition matrices; and (d) perform an independent component analysis to obtain a rotation matrix using one of the singular vector matrices generated by SVD from the matrix partitioned in accordance with the estimated period p and to calculate an independent component matrix and an associated component matrix one component matrix containing estimated separated signal modulation envelopes and the other containing estimated separated cyclets.

12. A non-transitory computer-readable medium embodying instructions for execution by computer apparatus, the instructions relating to separation of a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, the source signals having periodicities similar or equal to p, and the computer-readable medium incorporating program code for controlling computer apparatus to: (a) express the composite signal as a matrix having rows each of which is a respective segment of signal amplitude values and corresponds to a length of time associated with a signal cyclet; (b) decompose the matrix by decorrelation and normalisation to obtain decomposition results; and (c) perform ICA of the decomposition results to obtain at least one of estimated separated signal modulation envelopes and estimated separated signal cyclets.

13. A non-transitory computer-readable medium embodying instructions for execution by computer apparatus, the instructions relating to separation of a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, the source signals having periodicities similar or equal to p, the computer-readable medium incorporating program code for controlling computer apparatus to: (a) partition the composite signal into sections to provide respective rows of a partition matrix; (b) perform a singular value decomposition of the matrix to obtain two singular vector matrices and a singular value matrix; and (c) perform an independent component analysis of one of the singular vector matrices to obtain a rotation matrix and using the rotation matrix to calculate an independent component matrix and an associated component matrix , one matrix containing estimated separated signal modulation envelopes and the other matrix containing estimated separated cyclets.

14. A method of separating a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, each source signal having a respective period similar or equal to p, the method comprising using a computer apparatus to perform the steps of: (a) expressing the composite signal as a trial matrix having rows each of which is a respective segment of signal amplitude values and corresponds to a length of time associated with a signal cyclet with a trial period p′, (b) implementing a singular value decomposition of the trial matrix to generate two singular vector matrices and a singular value matrix, the trial matrix having a probability associated with its decomposition; and (c) iterating steps (a) and (b) for a series of different values of the trial period p′ to generate multiple versions of the trial matrix and associated probabilities; (d) performing independent component analysis (ICA) upon results obtained in the singular value decomposition of that version of the trial matrix associated with maximum probability and having signal cyclet of trial period p′ taken to be the period p subject to this period not corresponding to a multiple of a true period.

15. A method of separating a plurality of source signals from a composite signal expressed as a series of values of signal amplitude, each source signal having a respective period similar or equal to p, the method comprising using a computer apparatus to perform the steps of: (a) expressing the composite signal as a matrix having rows each of which is a respective segment of signal amplitude values and corresponds to a length of time associated with a signal cyclet; (b) implementing a decomposition of the matrix by decorrelation and normalisation to obtain decomposition results; (c) estimating a number q of source signals with periodicities similar or equal to p present within the composite signal and reducing the decomposition results in accordance with such number; and (d) performing independent component analysis (ICA) of the decomposition results to obtain at least one of estimated separated signal modulation envelopes and estimated separated signal cyclets.

16. A method according to claim 15 characterised in that the number q of source signals is estimated from the source signals' origins.

17. A method according to claim 15 characterised in that the number q of source signals is estimated from a number of elements of a singular value matrix, the elements having values exceeding a threshold value.